Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of x^(7/6)
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Derivative of x^4*e^x
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Derivative of e^x-7
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Derivative of (1-3x)^4
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Identical expressions
- sqrt6(x^ five)
- square root of 6(x to the power of 5)
- square root of 6(x to the power of five)
- √6(x^5)
- sqrt6(x5)
- sqrt6x5
- sqrt6(x⁵)
- sqrt6x^5
Derivative of sqrt6(x^5)
The solution
You have entered
[src]
0.166666666666667 / 5\ \x /
$$\left(x^{5}\right)^{0.166666666666667}$$
(x^5)^0.166666666666667
Detail solution
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Let .
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Apply the power rule: goes to
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Then, apply the chain rule. Multiply by :
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Apply the power rule: goes to
The result of the chain rule is:
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The answer is:
The first derivative
[src]
0.166666666666667
/ 5\
0.833333333333333*\x /
---------------------------------------
x
$$\frac{0.833333333333333 \left(x^{5}\right)^{0.166666666666667}}{x}$$
The second derivative
[src]
0.166666666666667
/ 5\
-0.138888888888889*\x /
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2
x
$$- \frac{0.138888888888889 \left(x^{5}\right)^{0.166666666666667}}{x^{2}}$$
The third derivative
[src]
0.166666666666667
/ 5\
0.162037037037037*\x /
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3
x
$$\frac{0.162037037037037 \left(x^{5}\right)^{0.166666666666667}}{x^{3}}$$
The graph